Data come from OpenACC (Anesiadou et al., 2020; Makridis et al., 2020), an open-access dataset created to benchmark ACC during normal operation in high-end consumer vehicles. The data were collected over multiple test-track and open-road tests. Metrics such as speed, acceleration, and headway were recorded from the CAN bus and additional sensors. The dataset was sampled at 10 Hz.

We selected the data from the test-track experiment at AstaZero in Sweden, because it was the only experiment in OpenACC that included a human control baseline, which was necessary to assess the relative safety benefit of driving with automation. The experiment consisted of a platoon of five vehicles on a traffic-free rural road. The first vehicle in the platoon occasionally perturbed the other vehicles by setting a different ACC target speed. Across trials, the following vehicles remained the same, but changed their relative order in the platoon. There was no other traffic on the test-track. The participants were professional drivers.

In all trials but one, the ACC’s time headway was set at the lowest (about 1.2 s); for consistency, we discarded the single trial that had the ACC headway set to high (above 2 s). While the headway setting may seem aggressive, users generally prefer a short time gap to reduce cut-ins (General Motors Corporation Research and Development Center, 2005, Ch. 4). We also kept only those driving segments where the minimum speed of the whole platoon was more than 30 km/h (the typical minimum operating speed of ACC) for at least 10 s, in order to assess steady-state (under regime) driving. Finally, the platoon was broken down into independent pairs of vehicles (e.g., the second and third vehicles in the platoon became the leader and follower vehicle, respectively) because we were interested in understanding rear-end crash scenarios rather than the effects on the whole platoon. We assumed that drivers would not anticipate the lead-vehicle actions by looking further ahead in the platoon. Additionally, we did not study ripple (string) effects from the behavior of the following vehicle to the vehicles behind. Overall, the amount of data we retained corresponded to approximately 888 km.

We used the brake threat number (BTN; Brännström et al., 2008) as a surrogate measure for lead-vehicle conflicts. BTN quantifies the brake effort needed to avoid a collision by comparing the minimum acceleration (maximum deceleration) required to avoid a collision (aminreq) and the minimum acceleration that the brake system is capable of (amin):

(1) B T N = a m i n r e q a m i n

with BTN in the (0,∞) domain. When BTN is greater than 1, the collision cannot be avoided as the required brake effort exceeds the brake capacity. Because BTN depends on braking behavior and performance, it is an improvement over the classic time to collision (TTC) measure (Daniel Åsljung et al., 2016).

We used a simplified brake profile. First, braking is applied after a delay td (Figure 1). Then, the acceleration decreases linearly with rate j. The braking capacity saturates when it reaches amin (Brännström et al., 2008). The specific ACC implementations and brake system characteristics of the vehicles in OpenACC are not publicly available. Therefore, we used reference values from current regulations or previous studies (Table 1). We did not include an AEB system to focus solely on the effect of ACC.

We computed BTN in the scenario where the lead vehicle maintains its current acceleration while the vehicle behind adapts its acceleration to avoid a collision (Figure 1). The BTN has a closed-form solution in some specific cases (Åsljung et al., 2017; Brännström et al., 2008). Here, we computed it as the solution to an optimization problem instead. This approach is more computationally demanding but more flexible, as it allows both vehicles to have any (continuous or piecewise) brake profile (see Appendix). We computed the BTN for all vehicles in the platoon at every second, given the current kinematic state of the vehicles from the data (a 1 Hz frequency was chosen to reduce computational cost). The time horizon was set to 30 s, to accommodate non-critical events. All BTN values less than or equal to zero indicate that the situation did not require braking and thus were excluded.

The values for BTN were analyzed with EVT to estimate the probability of a rear-end crash. The premise is that car-following is a set of circumstances that has a non-zero probability of ending up in a conflict, so that when the process is repeated enough times it will result in a crash. The assumption is that car following is a stationary process (Coles, 2001, Ch. 1). Crashes that are the result of exceptional lead-vehicle situations (e.g., a lead vehicle slamming on the brakes suddenly) are not considered in this analysis, as these situations would violate that assumption; the stability of the prevailing car-following process would be disrupted, and the situation would not be compatible with an EVT analysis.

Previous studies of real-world traffic have found that drivers often follow a lead vehicle too closely; the distance is too short for their typical perception-reaction time. Drivers need more than 1 s to brake (Lamble et al., 1999; Markkula et al., 2016; Summala, 2000; Summala et al., 1998), and the proportion of THW<1 s can be much higher under human control than with ACC (General Motors Corporation Research and Development Center, 2005, Ch. 8; Malta et al., 2012, Ch. 4; (Varotto et al., 2022), (Morando et al., 2019)). Thus, the potential safety benefit of an ACC that maintains adequate headway is considerable. However, the typical THW in the manual control data in the OpenACC experiment was around 2 s (the value recommended in driving manuals in many European countries Technical Group Road Safety, 2009). Consequently, the safety benefits of ACC in the OpenACC experiment were less pronounced or absent.

Driving is largely a self-paced task; drivers actively adapt their driving to maintain a comfortable safety boundary (Engström & Aust, 2011; Summala, 2007). During routine driving we may follow a vehicle too closely—intentionally because we are in a hurry or unintentionally because we don’t recognize that we are, in fact, too close (Taieb-Maimon & Shinar, 2001). In contrast, professional drivers in a controlled experiment may be more careful than usual because they are aware it is a test. This is one possible reason why our estimates are much more conservative than those of Åsljung, Nilsson, and Fredriksson (2017), despite using a similar method. In addition, Åsljung, Nilsson, and Fredriksson (2017) used a much larger FOT dataset (250.000 km vs. 888 km); they used professional drivers as well, but the data were from real traffic. Their best estimate was 3⋅106 km between collisions under manual control, which is close to the rear-end crash frequency in manual driving in motorways in Europe (around 1.3⋅106 km; Dobberstein et al., 2022, para. 6.2). The results of Åsljung, Nilsson, and Fredriksson (2017) are more precise than ours, but their paper also highlights how some modeling decisions can affect the results, particularly with extrapolations over long time horizons. Depending on the method used to fit their models, Åsljung, Nilsson, and Fredriksson (2017) obtained an estimate of 106 – 1010 km between crashes. Ultimately, Åsljung, Nilsson, and Fredriksson (2017) chose the model that yielded an estimate closer to the one from crash statistics, but without that reference, we would not know which model is best.

Because of the cautious manual driving and the absence of any external perturbations of the traffic flow, the conditions leading to our results are not the same as those we would observe in regular traffic; the difference is many orders of magnitude (2⋅10138 vs. 1.3⋅106 km in Dobberstein et al., 2022, para. 6.2). However, despite the small dataset, the model was a good fit to the data (Figures 5, 6, and 7), and the Bayesian model provided a more complete account of uncertainty than maximum likelihood estimates (Coles, 2001, Ch. 9). While the modeling approach shows promise, the available data were not representative of real-world driving behavior. The validity of the results depends on the quality of the input, thus, as with most techniques, agreement with the observed data is a necessary but not sufficient condition to justify long-term extrapolation (Coles, 2001, Ch. 3).

Crashes in manual driving happen for many reasons, including human factors such as inattention and distraction (National Center for Statistics and Analysis, 2022; Singh, 2015). As the professional drivers were careful, it is likely that the data in OpenACC did not include those human crash-contributing factors. In the future, one could supplement the data by simulating driver impairment with different braking parameters (cf. Table 1). For example, when everything else is kept constant, the driver’s response time is the most important parameter in our braking model. Thus, one could include a response time distribution and modulate it for different driver states. In this work, for convenience and reduced computational cost, we assumed that all drivers would recognize a hazard and start braking with a constant reaction time (see also UNECE, 2022, p. p. 30). However, analyses of crashes in naturalistic driving reveal that drivers’ responses depend on the urgency of the situation and their visual behavior, rather than being a fixed reaction time (Engström et al., 2022; Markkula et al., 2016; Summala, 2000). Moreover, many crashes happen because of a mismatch between drivers’ attention and a rapidly evolving traffic event (Summala, 2000; Victor et al., 2015). Thus, in future work, visual behavior could also be included (see Bärgman et al., 2015), but the computational demand would increase drastically.

There is little information on using EVT for the safety estimation of systems such as ACC. Most of the literature has focused on autonomous emergency interventions (e.g., AEB). Unlike ACC, AEB is usually active by default and is available in most new cars. ACC, instead, is a convenience system that drivers can choose to buy and use (or not). Even though the estimated crash frequency of ACC is higher than defensive manual driving, it is still extremely low—lower than the collision frequency of manual driving on motorways, which are the typical operational design domain of ACC (9⋅1015 vs. 1.3⋅106 km in Dobberstein et al., 2022, para. 6.2). ACC can, in fact, increase comfort and safety. It is also possible that the higher BM values under ACC in our analysis are the consequence of a deliberate delay in the system intended to prevent discomfort by avoiding adjusting the speed too frequently.

A platoon is an excellent driving situation for gathering data for an EVT analysis, since it provides data on prolonged car-following from multiple vehicles in a single short session. While there is less interference (e.g., due to sensor noise or cut-ins) on a test track than in real traffic, we can assume that ACC operates similarly in both environments. Moreover, the existing sources of interference may become less frequent during normal use as technology improves.

Many different threat metrics can be used as crash surrogates (Li et al., 2021; Westhofen et al., 2022). The most common one—especially in the EVT literature—is the TTC, although previous research has shown that BTN is better than TTC for studying rear-end crashes in manual driving (Åsljung et al., 2017). It is our opinion that proximity measures such as THW and TTC do not provide a useful comparison between automated and manual driving, since they do not account for differences in braking behavior and performance. For example, based on TTC alone, ACC would be less safe than manual driving just because it keeps a shorter headway (Figure 3); such analysis would ignore the fact that ACC is arguably more consistent and rapid at adjusting the distance to the lead vehicle than humans are. The advantage of BTN is that it also incorporates a braking profile, capturing some of the unique features of human control (e.g., brake reaction time; Table 1). Ideally, the brake profile would include additional system interventions (e.g., trigger warnings or autonomous interventions based on the developing lead vehicle conflict) which would not be possible with TTC alone.

Analyses based upon BTN may need to be complemented with other metrics. For example, Δv could be used to estimate the potential injury outcome of a crash (Bärgman et al., 2015; Kusano et al., 2022), since BTN does not provide this information. Unfortunately, Δv exists only when a collision has occurred, so it does not allow extrapolating from near-crashes to crashes, as BTN does. Nonetheless, future work could improve EVT models by including Δv, to estimate extreme severity crashes based on observed ones.

Alberto Morando: Conceptualization, Formal analysis, Methodology, Software, Visualization, Writing—original draft, Writing—review & editing.

The author is employed at Autoliv (www.autoliv.com), which is a company that develops, manufactures, and sells (among others) vehicle safety products.

None.

None.

Handling editor: Lai Zheng, Harbin Institute of Technology, China

Reviewers: Attila Borsos, University of Győr, Hungary; Zhankun Chen, Lund University, Sweden